11. MOEA#

import warnings; warnings.simplefilter('ignore')
!wget https://raw.githubusercontent.com/cfteach/modules/master/detector2.py 
!pip install pymoo > /dev/null 2>&1
!pip install plotly > /dev/null 2>&1
!pip install ipyvolume > /dev/null 2>&1
!pip install altair > /dev/null 2>&1
--2024-07-10 14:11:37--  https://raw.githubusercontent.com/cfteach/modules/master/detector2.py
Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.110.133, 185.199.111.133, 185.199.108.133, ...
Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.110.133|:443... connected.
HTTP request sent, awaiting response... 200 OK
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Saving to: ‘detector2.py.4’

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2024-07-10 14:11:37 (863 KB/s) - ‘detector2.py.4’ saved [7976/7976]
%load_ext autoreload
%autoreload 2


import os
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
#import AI4NP_detector_opt.sol2.detector2 as detector2
import detector2
from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.core.problem import Problem
from pymoo.optimize import minimize
from pymoo.visualization.scatter import Scatter
from pymoo.util.display.column import Column
from pymoo.util.display.output import Output

from pymoo.util.nds.non_dominated_sorting import NonDominatedSorting

11.1. Create detector geometry and simulate tracks#

The module detector creates a simple 2D geometry of a wire based tracker made by 4 planes.

The adjustable parameters are the radius of each wire, the pitch (along the y axis), and the shift along y and z of a plane with respect to the previous one.

A total of 8 parameters can be tuned.

The goal of this toy model, is to tune the detector design so to optimize the efficiency (fraction of tracks which are detected) as well as the cost for its realization. As a proxy for the cost, we use the material/volume (the surface in 2D) of the detector. For a track to be detetected, in the efficiency definition we require at least two wires hit by the track.

So we want to maximize the efficiency (defined in detector.py) and minimize the cost.

11.1.1. LIST OF PARAMETERS#

(baseline values)

  • R = .5 [cm]

  • pitch = 4.0 [cm]

  • y1 = 0.0, y2 = 0.0, y3 = 0.0, z1 = 2.0, z2 = 4.0, z3 = 6.0 [cm]

# CONSTANT PARAMETERS
#------ define mother region ------#
y_min=-10.1
y_max=10.1
N_tracks = 1000


print("::::: BASELINE PARAMETERS :::::")
R = 0.5
pitch = 4.0
y1 = 2.0
y2 = 1.0
y3 = 0.0
z1 = 2.0
z2 = 4.0
z3 = 6.0

print("R, pitch, y1, y2, y3, z1, z2, z3: ", R, pitch, y1, y2, y3, z1, z2, z3,"\n")


#------------- GEOMETRY ---------------#
print(":::: INITIAL GEOMETRY ::::")
tr = detector2.Tracker(R, pitch, y1, y2, y3, z1, z2, z3)
Z, Y = tr.create_geometry()
num_wires = detector2.calculate_wires(Y, y_min, y_max)

volume = detector2.wires_volume(Y, y_min, y_max,R)

detector2.geometry_display(Z, Y, R, y_min=y_min, y_max=y_max,block=False,pause=5) #5

print("# of wires: ", num_wires, ", volume: ", volume)

#------------- TRACK GENERATION -----------#
print(":::: TRACK GENERATION ::::")
t = detector2.Tracks(b_min=y_min, b_max=y_max, alpha_mean=0, alpha_std=0.2)
tracks = t.generate(N_tracks)

detector2.geometry_display(Z, Y, R, y_min=y_min, y_max=y_max,block=False, pause=-1)
detector2.tracks_display(tracks, Z,block=False,pause=-1)

 #a track is detected if at least two wires have been hit
score = detector2.get_score(Z, Y, tracks, R)
frac_detected = score[0]
resolution = score[1]
print("fraction of tracks detected: ",frac_detected)
print("resolution: ",resolution)
::::: BASELINE PARAMETERS :::::
R, pitch, y1, y2, y3, z1, z2, z3:  0.5 4.0 2.0 1.0 0.0 2.0 4.0 6.0 

:::: INITIAL GEOMETRY ::::
# of wires:  21 , volume:  65.94
:::: TRACK GENERATION ::::
../_images/8c341241735b12a95ab258fa56b0581691f8ced88b954fa55321ac5208318769.png ../_images/6f6bf5645b2c955c087e9e60591cf5159455c83e6eafcb106d27dded294e4e39.png
fraction of tracks detected:  0.243
resolution:  0.23594329069824552

11.2. Define Objectives#

Defines a class for the objectives of the problem that can be used in the MOO.

# The objectives are computed by setting up the geometry and 
# computing the values of the objectives. Mimicing a G4 type simulation
class objectives():

  def __init__(self,tracks,y_min,y_max):
    self.tracks = tracks
    self.y_min = y_min
    self.y_max = y_max

  def wrapper_geometry(fun):

      def inner(self):
          R, pitch, y1, y2, y3, z1, z2, z3 = self.X
          self.geometry(R, pitch, y1, y2, y3, z1, z2, z3)
          return fun(self)
      return inner

  def update_tracks(self, new_tracks):
    self.tracks = new_tracks

  def update_design_point(self,X):
      self.X = X


  def geometry(self,R, pitch, y1, y2, y3, z1, z2, z3):
    tr = detector2.Tracker(R, pitch, y1, y2, y3, z1, z2, z3)
    self.R = R
    self.Z, self.Y = tr.create_geometry()


  @wrapper_geometry
  def calc_score(self):
      res = detector2.get_score(self.Z, self.Y, self.tracks, self.R)
      assert res[0] >= 0 and res[1] >= 0,"Fraction or Resolution negative."

      return res


  def get_score(self,X):
    R, pitch, y1, y2, y3, z1, z2, z3 = X
    self.geometry(R, pitch, y1, y2, y3, z1, z2, z3)
    res = detector2.get_score(self.Z, self.Y, self.tracks, self.R)
    return res


  def get_volume(self):
    volume = detector2.wires_volume(self.Y, self.y_min, self.y_max,self.R)
    return volume



res = objectives(tracks,y_min,y_max)

#res.geometry(R, pitch, y1, y2, y3, z1, z2, z3)

X = R, pitch, y1, y2, y3, z1, z2, z3
#fscore  = res.get_score(X)
res.update_design_point(X)
fscore  = res.calc_score()[0]
fvolume = res.get_volume()

print("...check: ", fvolume, fscore)
...check:  65.94 0.243

11.3. Multi-Objective Optimization#

We will be using pymoo (https://pymoo.org/getting_started.html).

  • In the constructor method we specify number of variables N, objectives M, and constraint functions, as well as the lower and upper boundaries of each variable. In our toy model, these boundaries are taken in such a way that all solutions are feasible and no constraint function is needed. You can try to change this and introduce some constraint.

  • The _evaluate method takes a one-dimensional NumPy array x number of entries equal to n_var. This behavior is enabled by setting elementwise_evaluation=True while calling the super() method.

  • Notice that every function is minimized. Our efficiency is defined as an tracking inefficiency = 1 - efficiency

  • We add the resolution as a third objective. The average residual of the track hit from the wire centre is used as a proxy for the resolution for this toy-model

from pymoo.core.problem import ElementwiseProblem
class MyProblem(ElementwiseProblem):

    #--------- vectorized ---------#

    def __init__(self, n_var=8, n_obj=2, n_constr=0, 
                 xl=np.array([0.5,2.5,0.,0.,0.,2.,2.,2.]), 
                 xu=np.array([1.0,5.0,4.,4.,4.,10.,10.,10.])
                 ):
        super().__init__(n_var=n_var, n_obj=n_obj, n_constr=n_constr, xl=xl, xu=xu)

    def _evaluate(self, x, out, *args, **kwargs):


        f1 = 1.- res.get_score(x)[0] # Ineffiency
        f2 = res.get_volume() # volume 
        #f3 = res.get_score(x)[1] #resolution

        out["F"] = [f1, f2]#, f3]

11.4. Creation of Problem and choice of optimization algorithm.#

  • We will use NSGA-II, as explained in the lectures. You can decide the population size and the number of offsprings, based on what we discussed.

  • Pymoo offers different algorithms that can be used which are highly customizable and can be easily extended. https://pymoo.org/algorithms/index.html

  • Before dealing with a problem, it’s useful to compare with a list of test problems reported in https://pymoo.org/problems/index.html, where different scenarios in terms of Variables, Objectives, Constraints are described.

n_var = 8 # number of design variables
n_obj = 2 # number of objectives
n_constr = 0 # number of constraints
xl = np.array([0.5,2.5,0.,0.,0.,2.,2.,2.]) # lower bounds of the problem, pitch, diameter, y1, y2, y3, z1, z2, z3
xu = np.array([1.0,5.0,4.,4.,4.,10.,10.,10.]) # upper bounds of the problem, pitch, diameter, y1, y2, y3, z1, z2, z3
pop_size = 40
n_offsprings=10

problem = MyProblem(n_var=n_var, n_obj=n_obj, n_constr=n_constr, xl=xl, xu=xu)



from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.operators.crossover.sbx import SBX
from pymoo.operators.mutation.pm import PM
from pymoo.operators.sampling.rnd import FloatRandomSampling
from pymoo.termination import get_termination
from pymoo.termination.xtol import DesignSpaceTermination
from pymoo.termination.robust import RobustTermination


# check out other sampling methods here https://pymoo.org/operators/sampling.html
# check out other crossover methods here https://pymoo.org/operators/crossover.html

algorithm = NSGA2(pop_size=pop_size,n_offsprings=10) 
crossover = SBX(prob=1.0, eta=1)
mutation = PM(eta=1)
termination = RobustTermination(DesignSpaceTermination(tol=0.01), period=20)
res = minimize(problem,
               algorithm,
               crossover = crossover,
               mutation = mutation,
               termination = termination,
               verbose=True,
               seed=1,
               save_history=True # Saves all of the history of the algorithm
               )
Compiled modules for significant speedup can not be used!
https://pymoo.org/installation.html#installation

To disable this warning:
from pymoo.config import Config
Config.warnings['not_compiled'] = False

==========================================================
n_gen  |  n_eval  | n_nds  |      eps      |   indicator  
==========================================================
     1 |       40 |     11 |             - |             -
     2 |       50 |     11 |  0.0027413883 |             f
     3 |       60 |     12 |  0.0947546531 |         ideal
     4 |       70 |     12 |  0.0072341683 |             f
     5 |       80 |     12 |  0.0436893204 |         ideal
     6 |       90 |     15 |  0.1030478955 |         ideal
     7 |      100 |     15 |  0.0031563673 |             f
     8 |      110 |     18 |  0.0063748159 |             f
     9 |      120 |     20 |  0.0587431694 |         ideal
    10 |      130 |     21 |  0.0093548023 |             f
    11 |      140 |     20 |  0.0020407572 |             f
    12 |      150 |     24 |  0.0072690067 |             f
    13 |      160 |     24 |  0.0309859155 |         nadir
    14 |      170 |     26 |  0.0042075736 |         ideal
    15 |      180 |     30 |  0.0027972028 |         ideal
    16 |      190 |     34 |  0.0020349296 |             f
    17 |      200 |     34 |  0.0199714693 |         nadir
    18 |      210 |     36 |  0.0039945972 |         ideal
    19 |      220 |     36 |  0.0009826153 |             f
    20 |      230 |     37 |  0.0037579662 |             f
    21 |      240 |     35 |  0.0014592392 |             f
    22 |      250 |     34 |  0.0352112676 |         nadir
    23 |      260 |     36 |  0.0353260870 |         nadir
    24 |      270 |     38 |  0.0080862534 |         ideal
    25 |      280 |     39 |  0.0022170657 |             f
    26 |      290 |     40 |  0.0039631531 |             f
    27 |      300 |     40 |  0.0022072120 |             f
    28 |      310 |     40 |  0.0026901414 |             f
    29 |      320 |     40 |  0.0001835229 |             f
    30 |      330 |     39 |  0.0010234613 |             f
    31 |      340 |     40 |  0.0024187426 |             f
    32 |      350 |     40 |  0.0940170940 |         nadir
    33 |      360 |     40 |  0.0023293560 |             f
    34 |      370 |     38 |  0.0049079755 |         nadir
    35 |      380 |     37 |  0.0502577320 |         nadir
    36 |      390 |     36 |  0.0006563741 |             f
    37 |      400 |     37 |  0.0017141003 |             f
    38 |      410 |     36 |  0.0028712323 |             f
    39 |      420 |     38 |  0.0021173840 |             f
    40 |      430 |     36 |  0.0038759690 |         nadir
    41 |      440 |     37 |  0.0026562484 |             f
    42 |      450 |     37 |  0.0002446164 |             f
    43 |      460 |     37 |  0.0004890469 |             f
    44 |      470 |     39 |  0.0017601127 |             f
    45 |      480 |     40 |  0.0065019506 |         nadir
    46 |      490 |     40 |  0.0004439410 |             f
    47 |      500 |     39 |  0.0006887275 |             f
    48 |      510 |     39 |  0.0012391439 |             f
    49 |      520 |     40 |  0.0023172797 |             f
    50 |      530 |     40 |  0.0051746442 |         ideal
    51 |      540 |     40 |  0.0025025970 |             f
    52 |      550 |     40 |  0.0009235842 |             f
    53 |      560 |     40 |  0.0008954103 |             f
    54 |      570 |     40 |  0.0020176739 |             f
    55 |      580 |     40 |  0.0040757161 |             f
    56 |      590 |     40 |  0.0004559372 |             f
    57 |      600 |     40 |  0.0009343304 |             f
    58 |      610 |     40 |  0.0016153460 |             f
    59 |      620 |     39 |  0.0032396179 |             f
    60 |      630 |     40 |  0.0007352798 |             f
    61 |      640 |     40 |  0.0007373257 |             f
    62 |      650 |     40 |  0.0016143712 |             f
    63 |      660 |     40 |  0.0025490394 |             f
    64 |      670 |     40 |  0.0005419965 |             f
    65 |      680 |     40 |  0.0010764221 |             f
    66 |      690 |     40 |  0.0018836599 |             f
    67 |      700 |     40 |  0.0024873428 |             f
    68 |      710 |     40 |  0.0032397454 |             f
    69 |      720 |     40 |  0.0025806452 |         ideal
    70 |      730 |     40 |  0.0001290855 |             f
    71 |      740 |     38 |  0.0025740026 |         ideal
    72 |      750 |     39 |  0.0051746442 |         nadir
    73 |      760 |     40 |  0.0004228679 |             f
    74 |      770 |     40 |  0.0006772112 |             f
    75 |      780 |     40 |  0.0007087106 |             f
    76 |      790 |     40 |  0.0007733101 |             f
    77 |      800 |     40 |  0.0017283666 |             f
    78 |      810 |     40 |  0.0026481686 |             f
    79 |      820 |     40 |  0.0014715193 |             f
    80 |      830 |     40 |  0.0020533503 |             f
    81 |      840 |     40 |  0.0022663095 |             f
    82 |      850 |     40 |  0.0047945855 |             f
    83 |      860 |     40 |  0.0012918488 |             f
    84 |      870 |     40 |  0.0016794457 |             f
    85 |      880 |     40 |  0.0028232935 |             f
    86 |      890 |     40 |  0.0005567317 |             f
    87 |      900 |     40 |  0.0009532404 |             f
    88 |      910 |     40 |  0.0012762379 |             f
    89 |      920 |     40 |  0.0017795763 |             f
    90 |      930 |     40 |  0.0023111541 |             f
    91 |      940 |     40 |  0.0025372523 |             f
    92 |      950 |     40 |  0.000000E+00 |             f
    93 |      960 |     40 |  0.0016059072 |             f
    94 |      970 |     40 |  0.0028795184 |             f
    95 |      980 |     40 |  0.0007938843 |             f
    96 |      990 |     40 |  0.0013896313 |             f
    97 |     1000 |     40 |  0.0018212966 |             f
    98 |     1010 |     40 |  0.0021702896 |             f
    99 |     1020 |     40 |  0.0024489872 |             f
   100 |     1030 |     40 |  0.0026427857 |             f
   101 |     1040 |     40 |  0.0003481081 |             f
   102 |     1050 |     38 |  0.0016148559 |             f
   103 |     1060 |     40 |  0.0037092973 |             f
   104 |     1070 |     40 |  0.0006885178 |             f
   105 |     1080 |     40 |  0.0008242412 |             f
   106 |     1090 |     40 |  0.0017915888 |             f
   107 |     1100 |     40 |  0.0019532965 |             f
   108 |     1110 |     40 |  0.0030048230 |             f
   109 |     1120 |     40 |  0.0001617076 |             f
   110 |     1130 |     40 |  0.0003670119 |             f
   111 |     1140 |     40 |  0.0003670119 |             f
   112 |     1150 |     40 |  0.0003670119 |             f
   113 |     1160 |     39 |  0.0005852633 |             f
   114 |     1170 |     40 |  0.0010142581 |             f
   115 |     1180 |     40 |  0.0016647951 |             f
   116 |     1190 |     40 |  0.0031320079 |             f
   117 |     1200 |     40 |  0.000000E+00 |             f
   118 |     1210 |     40 |  0.0000659278 |             f
   119 |     1220 |     40 |  0.0377774021 |         nadir
   120 |     1230 |     40 |  0.0737878852 |         nadir
   121 |     1240 |     40 |  0.0016480051 |             f
   122 |     1250 |     40 |  0.0019964714 |             f
   123 |     1260 |     40 |  0.0025344208 |             f
   124 |     1270 |     40 |  0.0005878600 |             f
   125 |     1280 |     40 |  0.0128018963 |         nadir
   126 |     1290 |     40 |  0.000000E+00 |             f
   127 |     1300 |     40 |  0.0006540880 |             f
   128 |     1310 |     40 |  0.0006540880 |             f
   129 |     1320 |     40 |  0.0013938250 |             f
   130 |     1330 |     40 |  0.0104302477 |         nadir
   131 |     1340 |     40 |  0.0003810035 |             f
   132 |     1350 |     40 |  0.0050893015 |         nadir
   133 |     1360 |     40 |  0.0004116133 |             f
   134 |     1370 |     40 |  0.0008813217 |             f
   135 |     1380 |     39 |  0.0017824396 |             f
   136 |     1390 |     39 |  0.0020500669 |             f
   137 |     1400 |     40 |  0.0204342273 |         nadir
   138 |     1410 |     40 |  0.0016223997 |             f
   139 |     1420 |     40 |  0.0016159771 |             f
   140 |     1430 |     40 |  0.0019855067 |             f
   141 |     1440 |     40 |  0.0031055978 |             f
   142 |     1450 |     40 |  0.0000319285 |             f
   143 |     1460 |     40 |  0.0007717300 |             f
   144 |     1470 |     40 |  0.0018380253 |             f
   145 |     1480 |     40 |  0.0032152230 |             f
   146 |     1490 |     40 |  0.0003831667 |             f
   147 |     1500 |     40 |  0.0014819364 |             f
   148 |     1510 |     40 |  0.0013322177 |             f
   149 |     1520 |     40 |  0.0013322177 |             f
   150 |     1530 |     40 |  0.0014604268 |             f
   151 |     1540 |     40 |  0.0014439883 |             f
   152 |     1550 |     39 |  0.0024449731 |             f
   153 |     1560 |     39 |  0.0024449731 |             f
   154 |     1570 |     40 |  0.0025966134 |             f
   155 |     1580 |     40 |  0.0009963924 |             f
   156 |     1590 |     40 |  0.0011991239 |             f
   157 |     1600 |     40 |  0.0011991239 |             f
   158 |     1610 |     40 |  0.0015260952 |             f
   159 |     1620 |     40 |  0.0015637512 |             f
   160 |     1630 |     40 |  0.0033488555 |             f
   161 |     1640 |     40 |  0.0002064141 |             f
   162 |     1650 |     40 |  0.0007431454 |             f
   163 |     1660 |     40 |  0.0007431454 |             f
   164 |     1670 |     40 |  0.0007432194 |             f
   165 |     1680 |     40 |  0.0008714189 |             f
   166 |     1690 |     40 |  0.0008714189 |             f
   167 |     1700 |     40 |  0.0022613064 |             f
   168 |     1710 |     40 |  0.0027845635 |             f
   169 |     1720 |     40 |  0.0003325095 |             f
   170 |     1730 |     40 |  0.0003325095 |             f
   171 |     1740 |     40 |  0.0003325095 |             f
   172 |     1750 |     40 |  0.0168831169 |         nadir
   173 |     1760 |     40 |  0.0001457224 |             f
   174 |     1770 |     40 |  0.0006333815 |             f
   175 |     1780 |     40 |  0.0243074209 |         nadir
   176 |     1790 |     40 |  0.0039062500 |         nadir
   177 |     1800 |     40 |  0.0007871277 |             f
   178 |     1810 |     40 |  0.0007871277 |             f
   179 |     1820 |     40 |  0.0013405341 |             f
   180 |     1830 |     40 |  0.0014707636 |             f
   181 |     1840 |     40 |  0.0018346456 |             f
   182 |     1850 |     40 |  0.0024717155 |             f
   183 |     1860 |     40 |  0.0025993989 |             f
   184 |     1870 |     40 |  0.0006426772 |             f
   185 |     1880 |     40 |  0.0013358068 |             f
   186 |     1890 |     40 |  0.0016482430 |             f
   187 |     1900 |     40 |  0.0018389517 |             f
   188 |     1910 |     40 |  0.0018715462 |             f
   189 |     1920 |     40 |  0.0021652485 |             f
   190 |     1930 |     40 |  0.0023400964 |             f
   191 |     1940 |     40 |  0.0027679556 |             f
   192 |     1950 |     40 |  0.000000E+00 |             f
   193 |     1960 |     40 |  0.0006018343 |             f
   194 |     1970 |     40 |  0.0008747707 |             f
   195 |     1980 |     40 |  0.0013667973 |             f
   196 |     1990 |     40 |  0.0013667973 |             f
   197 |     2000 |     40 |  0.0016761886 |             f
   198 |     2010 |     40 |  0.0017413777 |             f
   199 |     2020 |     40 |  0.0026572064 |             f
   200 |     2030 |     40 |  0.0000688098 |             f
   201 |     2040 |     40 |  0.0008445565 |             f
   202 |     2050 |     40 |  0.0009749648 |             f
   203 |     2060 |     40 |  0.0014942860 |             f
   204 |     2070 |     40 |  0.0025934720 |             f
   205 |     2080 |     40 |  0.0017401394 |             f
   206 |     2090 |     40 |  0.0023221061 |             f
   207 |     2100 |     40 |  0.0023872952 |             f
   208 |     2110 |     40 |  0.0025176733 |             f
   209 |     2120 |     40 |  0.0004807714 |             f
   210 |     2130 |     40 |  0.0007745111 |             f
   211 |     2140 |     40 |  0.0009700783 |             f
   212 |     2150 |     40 |  0.0013126845 |             f
   213 |     2160 |     40 |  0.0013452790 |             f
   214 |     2170 |     40 |  0.0018874618 |             f
   215 |     2180 |     40 |  0.0018874618 |             f
   216 |     2190 |     40 |  0.0368806910 |         nadir
   217 |     2200 |     40 |  0.0004070798 |             f
   218 |     2210 |     40 |  0.0004746520 |             f
   219 |     2220 |     40 |  0.0004746520 |             f
   220 |     2230 |     40 |  0.0004746520 |             f
   221 |     2240 |     40 |  0.0008422564 |             f
   222 |     2250 |     40 |  0.0017545221 |             f
   223 |     2260 |     40 |  0.0020153015 |             f
   224 |     2270 |     40 |  0.0025819638 |             f
   225 |     2280 |     40 |  0.0000894849 |             f
   226 |     2290 |     40 |  0.0026007802 |         ideal
   227 |     2300 |     40 |  0.0018032340 |             f
   228 |     2310 |     40 |  0.0018357438 |             f
   229 |     2320 |     40 |  0.0020486880 |             f
   230 |     2330 |     40 |  0.0022122668 |             f
   231 |     2340 |     40 |  0.0031322586 |             f
   232 |     2350 |     40 |  0.0010404021 |             f
   233 |     2360 |     40 |  0.0010404021 |             f
   234 |     2370 |     40 |  0.0014305192 |             f
   235 |     2380 |     40 |  0.0018711851 |             f
   236 |     2390 |     40 |  0.0018386788 |             f
   237 |     2400 |     40 |  0.0026209920 |             f
   238 |     2410 |     40 |  0.0007648256 |             f
   239 |     2420 |     40 |  0.0009553363 |             f
   240 |     2430 |     40 |  0.0009553363 |             f
   241 |     2440 |     40 |  0.0017599982 |             f
   242 |     2450 |     40 |  0.0021877392 |             f
   243 |     2460 |     40 |  0.0021877392 |             f
   244 |     2470 |     40 |  0.0022591629 |             f
   245 |     2480 |     40 |  0.0022591629 |             f
   246 |     2490 |     40 |  0.0650969529 |         nadir
   247 |     2500 |     40 |  0.0000692521 |             f
   248 |     2510 |     40 |  0.0010452080 |             f
   249 |     2520 |     40 |  0.0010452212 |             f
   250 |     2530 |     40 |  0.0015283975 |             f
   251 |     2540 |     40 |  0.0022967201 |             f
   252 |     2550 |     40 |  0.0022967201 |             f
   253 |     2560 |     40 |  0.0025225513 |             f
   254 |     2570 |     40 |  0.0004348303 |             f
   255 |     2580 |     40 |  0.0014622455 |             f
   256 |     2590 |     40 |  0.0027777778 |         nadir
   257 |     2600 |     40 |  0.0001908054 |             f
   258 |     2610 |     40 |  0.0001908054 |             f
   259 |     2620 |     40 |  0.0011531573 |             f
   260 |     2630 |     40 |  0.0016783769 |             f
   261 |     2640 |     40 |  0.0023042212 |             f
   262 |     2650 |     40 |  0.0024165382 |             f
   263 |     2660 |     40 |  0.0022032060 |             f
   264 |     2670 |     40 |  0.0031104250 |             f
   265 |     2680 |     40 |  0.0006368345 |             f
   266 |     2690 |     40 |  0.0005684804 |             f
   267 |     2700 |     40 |  0.0005684804 |             f
   268 |     2710 |     40 |  0.0010810845 |             f
   269 |     2720 |     40 |  0.0016093270 |             f
   270 |     2730 |     40 |  0.0021396112 |             f
   271 |     2740 |     40 |  0.0022090556 |             f
   272 |     2750 |     40 |  0.0022090556 |             f
   273 |     2760 |     40 |  0.0028663403 |             f
   274 |     2770 |     40 |  0.000000E+00 |             f
   275 |     2780 |     40 |  0.000000E+00 |             f
   276 |     2790 |     40 |  0.0005223004 |             f
   277 |     2800 |     40 |  0.0008139673 |             f
   278 |     2810 |     40 |  0.0008139673 |             f
   279 |     2820 |     40 |  0.0008139673 |             f
   280 |     2830 |     40 |  0.0018244143 |             f
   281 |     2840 |     40 |  0.0637191157 |         nadir
   282 |     2850 |     40 |  0.0002857970 |             f
   283 |     2860 |     40 |  0.0011833511 |             f
   284 |     2870 |     40 |  0.0012158609 |             f
   285 |     2880 |     40 |  0.0012158609 |             f
   286 |     2890 |     40 |  0.0012483706 |             f
   287 |     2900 |     40 |  0.0013458999 |             f
   288 |     2910 |     40 |  0.0029587385 |             f
   289 |     2920 |     40 |  0.000000E+00 |             f
   290 |     2930 |     40 |  0.0065445026 |         nadir
   291 |     2940 |     40 |  0.0010669156 |             f
   292 |     2950 |     40 |  0.0023102327 |             f
   293 |     2960 |     40 |  0.0033631678 |             f
   294 |     2970 |     40 |  0.0000786314 |             f
   295 |     2980 |     40 |  0.0002750071 |             f
   296 |     2990 |     40 |  0.0010600204 |             f
   297 |     3000 |     40 |  0.0010600204 |             f
   298 |     3010 |     40 |  0.0010600204 |             f
   299 |     3020 |     40 |  0.0014365407 |             f
   300 |     3030 |     40 |  0.0014692632 |             f
   301 |     3040 |     40 |  0.0017521710 |             f
   302 |     3050 |     40 |  0.0019661456 |             f
   303 |     3060 |     40 |  0.0021627380 |             f
   304 |     3070 |     40 |  0.0021627380 |             f
   305 |     3080 |     40 |  0.0021627380 |             f
   306 |     3090 |     40 |  0.0022132248 |             f
   307 |     3100 |     40 |  0.0023116020 |             f
   308 |     3110 |     40 |  0.0024098982 |             f
   309 |     3120 |     40 |  0.0026720214 |             f
   310 |     3130 |     40 |  0.0001965924 |             f
   311 |     3140 |     40 |  0.0039473684 |         nadir
   312 |     3150 |     40 |  0.0002956075 |             f
   313 |     3160 |     40 |  0.0008823225 |             f
   314 |     3170 |     40 |  0.0008823225 |             f
   315 |     3180 |     40 |  0.0015405343 |             f
   316 |     3190 |     40 |  0.0015405343 |             f
   317 |     3200 |     40 |  0.0017206313 |             f
   318 |     3210 |     40 |  0.0021134568 |             f
   319 |     3220 |     40 |  0.0021134568 |             f
   320 |     3230 |     40 |  0.0021134568 |             f
   321 |     3240 |     40 |  0.0021792462 |             f
   322 |     3250 |     40 |  0.0027287529 |             f
   323 |     3260 |     40 |  0.000000E+00 |             f
   324 |     3270 |     40 |  0.0001197069 |             f
   325 |     3280 |     40 |  0.0001197069 |             f
   326 |     3290 |     40 |  0.0009392685 |             f
   327 |     3300 |     40 |  0.0011037422 |             f
   328 |     3310 |     40 |  0.0011037422 |             f
   329 |     3320 |     40 |  0.0011037422 |             f
   330 |     3330 |     40 |  0.0015740683 |             f
   331 |     3340 |     40 |  0.0015935613 |             f
   332 |     3350 |     40 |  0.0017637782 |             f
   333 |     3360 |     40 |  0.0019294538 |             f
   334 |     3370 |     40 |  0.0023059640 |             f
   335 |     3380 |     40 |  0.0028772907 |             f
   336 |     3390 |     40 |  0.0004946330 |             f
   337 |     3400 |     40 |  0.0015434352 |             f
   338 |     3410 |     40 |  0.0017644506 |             f
   339 |     3420 |     40 |  0.0017644506 |             f
   340 |     3430 |     40 |  0.0018798936 |             f
   341 |     3440 |     40 |  0.0018798936 |             f
   342 |     3450 |     40 |  0.0029230329 |             f
   343 |     3460 |     40 |  0.0002149308 |             f
   344 |     3470 |     40 |  0.0002332633 |             f
   345 |     3480 |     40 |  0.0092961487 |         nadir
   346 |     3490 |     40 |  0.000000E+00 |             f
   347 |     3500 |     40 |  0.0004565130 |             f
   348 |     3510 |     40 |  0.0015263368 |             f
   349 |     3520 |     40 |  0.0026704886 |             f
   350 |     3530 |     40 |  0.0000332005 |             f
   351 |     3540 |     40 |  0.0000462447 |             f
   352 |     3550 |     40 |  0.0000462447 |             f
   353 |     3560 |     40 |  0.0000462447 |             f
   354 |     3570 |     40 |  0.0000462447 |             f
   355 |     3580 |     40 |  0.0008945736 |             f
   356 |     3590 |     40 |  0.0012073516 |             f
   357 |     3600 |     40 |  0.0012134750 |             f
   358 |     3610 |     40 |  0.0016355172 |             f
   359 |     3620 |     40 |  0.0026631158 |         nadir
   360 |     3630 |     40 |  0.0005496998 |             f
   361 |     3640 |     40 |  0.0010930583 |             f
   362 |     3650 |     40 |  0.0009781031 |             f
   363 |     3660 |     40 |  0.0011399979 |             f
   364 |     3670 |     40 |  0.0011399979 |             f
   365 |     3680 |     40 |  0.0014143969 |             f
   366 |     3690 |     40 |  0.0018771532 |             f
   367 |     3700 |     40 |  0.0018771532 |             f
   368 |     3710 |     40 |  0.0018782311 |             f
   369 |     3720 |     40 |  0.0017811649 |             f
   370 |     3730 |     40 |  0.0022183128 |             f
   371 |     3740 |     40 |  0.0022183128 |             f
   372 |     3750 |     40 |  0.0022524937 |             f
   373 |     3760 |     40 |  0.0023219231 |             f
   374 |     3770 |     40 |  0.0023219231 |             f
   375 |     3780 |     40 |  0.0020146673 |             f
   376 |     3790 |     40 |  0.0020146673 |             f
   377 |     3800 |     40 |  0.0021545346 |             f
   378 |     3810 |     40 |  0.0021545346 |             f
   379 |     3820 |     40 |  0.0025184691 |             f
   380 |     3830 |     40 |  0.0004660453 |             f
   381 |     3840 |     40 |  0.0009424448 |             f
   382 |     3850 |     40 |  0.0009424448 |             f
   383 |     3860 |     40 |  0.0010090227 |             f
   384 |     3870 |     40 |  0.0015417986 |             f
   385 |     3880 |     40 |  0.0015750875 |             f
   386 |     3890 |     40 |  0.0018634731 |             f
   387 |     3900 |     40 |  0.0026703535 |             f
   388 |     3910 |     40 |  0.000000E+00 |             f
   389 |     3920 |     40 |  0.0000942910 |             f
   390 |     3930 |     40 |  0.0000942910 |             f
   391 |     3940 |     40 |  0.0005720457 |             f
   392 |     3950 |     40 |  0.0007384978 |             f
   393 |     3960 |     40 |  0.0013709878 |             f
   394 |     3970 |     40 |  0.0018508980 |             f
   395 |     3980 |     40 |  0.0024441047 |             f
   396 |     3990 |     40 |  0.0020723041 |             f
   397 |     4000 |     40 |  0.0023851478 |             f
   398 |     4010 |     40 |  0.0027177042 |             f
   399 |     4020 |     40 |  0.0000332889 |             f
   400 |     4030 |     40 |  0.0004501224 |             f
   401 |     4040 |     40 |  0.0004834114 |             f
   402 |     4050 |     40 |  0.0004834114 |             f
   403 |     4060 |     40 |  0.0005499893 |             f
   404 |     4070 |     40 |  0.0010150487 |             f
   405 |     4080 |     40 |  0.0011428554 |             f
   406 |     4090 |     40 |  0.0012057996 |             f
   407 |     4100 |     40 |  0.0012097684 |             f
   408 |     4110 |     40 |  0.0012097684 |             f
   409 |     4120 |     40 |  0.0013951153 |             f
   410 |     4130 |     40 |  0.0013951153 |             f
   411 |     4140 |     40 |  0.0012644876 |             f
   412 |     4150 |     40 |  0.0012644876 |             f
   413 |     4160 |     40 |  0.0017945810 |             f
   414 |     4170 |     40 |  0.0025779570 |             f
   415 |     4180 |     40 |  0.000000E+00 |             f
   416 |     4190 |     40 |  0.000000E+00 |             f
   417 |     4200 |     40 |  0.0005149009 |             f
   418 |     4210 |     40 |  0.0012489215 |             f
   419 |     4220 |     40 |  0.0012822104 |             f
   420 |     4230 |     40 |  0.0012822104 |             f
   421 |     4240 |     40 |  0.0014939228 |             f
   422 |     4250 |     40 |  0.0231607629 |         nadir
   423 |     4260 |     40 |  0.0082417582 |         nadir
   424 |     4270 |     40 |  0.0013249670 |             f
   425 |     4280 |     40 |  0.0014123489 |             f
   426 |     4290 |     40 |  0.0016414622 |             f
   427 |     4300 |     40 |  0.0019378640 |             f
   428 |     4310 |     40 |  0.0041379310 |         nadir
   429 |     4320 |     40 |  0.0002485656 |             f
   430 |     4330 |     40 |  0.0006244975 |             f
   431 |     4340 |     40 |  0.0006244975 |             f
   432 |     4350 |     40 |  0.0007969113 |             f
   433 |     4360 |     40 |  0.0010804801 |             f
   434 |     4370 |     40 |  0.0015284488 |             f
   435 |     4380 |     40 |  0.0015284488 |             f
   436 |     4390 |     40 |  0.0016645937 |             f
   437 |     4400 |     40 |  0.0018763920 |             f
   438 |     4410 |     40 |  0.0020143230 |             f
   439 |     4420 |     40 |  0.0030094232 |             f
   440 |     4430 |     40 |  0.0002766015 |             f
   441 |     4440 |     40 |  0.0013389243 |             f
   442 |     4450 |     40 |  0.0015307119 |             f
   443 |     4460 |     39 |  0.0024431191 |             f
   444 |     4470 |     40 |  0.0035460569 |             f
   445 |     4480 |     40 |  0.0000344828 |             f
   446 |     4490 |     40 |  0.0003103448 |             f
   447 |     4500 |     40 |  0.0010816217 |             f
   448 |     4510 |     40 |  0.0010816217 |             f
   449 |     4520 |     40 |  0.0011161044 |             f
   450 |     4530 |     40 |  0.0014650275 |             f
   451 |     4540 |     40 |  0.0018040329 |             f
   452 |     4550 |     40 |  0.0015281708 |             f
   453 |     4560 |     40 |  0.0015626536 |             f
   454 |     4570 |     40 |  0.0015626536 |             f
   455 |     4580 |     40 |  0.0021219432 |             f
   456 |     4590 |     40 |  0.0021219432 |             f
   457 |     4600 |     40 |  0.0022900318 |             f
   458 |     4610 |     40 |  0.0028647504 |             f
   459 |     4620 |     40 |  0.0016946470 |             f
   460 |     4630 |     40 |  0.0016946470 |             f
   461 |     4640 |     40 |  0.0022474960 |             f
   462 |     4650 |     40 |  0.0019597009 |             f
   463 |     4660 |     40 |  0.0020370307 |             f
   464 |     4670 |     40 |  0.0030387175 |             f
   465 |     4680 |     40 |  0.0008135850 |             f
   466 |     4690 |     40 |  0.0010561837 |             f
   467 |     4700 |     40 |  0.0026045398 |         nadir
   468 |     4710 |     40 |  0.0005265134 |             f
   469 |     4720 |     40 |  0.000000E+00 |             f
   470 |     4730 |     40 |  0.000000E+00 |             f
   471 |     4740 |     40 |  0.0004267321 |             f
   472 |     4750 |     40 |  0.0004267321 |             f
   473 |     4760 |     40 |  0.0004267321 |             f
   474 |     4770 |     40 |  0.0005644731 |             f
   475 |     4780 |     40 |  0.0008990480 |             f
   476 |     4790 |     40 |  0.0011093252 |             f
   477 |     4800 |     40 |  0.0014691939 |             f
   478 |     4810 |     40 |  0.0016413702 |             f
   479 |     4820 |     40 |  0.0018059209 |             f
   480 |     4830 |     40 |  0.0018403561 |             f
   481 |     4840 |     40 |  0.0018403561 |             f
   482 |     4850 |     40 |  0.0023079316 |             f
   483 |     4860 |     40 |  0.0023079316 |             f
   484 |     4870 |     40 |  0.0023079316 |             f
   485 |     4880 |     40 |  0.0024112579 |             f
   486 |     4890 |     40 |  0.0024112579 |             f
   487 |     4900 |     40 |  0.0024112579 |             f
   488 |     4910 |     39 |  0.0111420613 |         nadir
   489 |     4920 |     40 |  0.0002442044 |             f
   490 |     4930 |     40 |  0.0002442044 |             f
   491 |     4940 |     40 |  0.0007486258 |             f
   492 |     4950 |     40 |  0.0008530826 |             f
   493 |     4960 |     40 |  0.0008530826 |             f
   494 |     4970 |     40 |  0.0012709109 |             f
   495 |     4980 |     40 |  0.0019405596 |             f
   496 |     4990 |     40 |  0.0020669659 |             f
   497 |     5000 |     40 |  0.0028277074 |             f
   498 |     5010 |     40 |  0.0005571034 |             f
   499 |     5020 |     40 |  0.0005571034 |             f
   500 |     5030 |     40 |  0.0005571034 |             f
   501 |     5040 |     40 |  0.0013652274 |             f
   502 |     5050 |     40 |  0.0015393515 |             f
   503 |     5060 |     40 |  0.0015393573 |             f
   504 |     5070 |     40 |  0.0020811082 |             f
   505 |     5080 |     40 |  0.0026046626 |             f
   506 |     5090 |     40 |  0.0003588780 |             f
   507 |     5100 |     40 |  0.0004653687 |             f
   508 |     5110 |     40 |  0.0002763608 |             f
   509 |     5120 |     40 |  0.0005557271 |             f
   510 |     5130 |     40 |  0.0012060635 |             f
   511 |     5140 |     40 |  0.0018102724 |             f
   512 |     5150 |     40 |  0.0018102724 |             f
   513 |     5160 |     40 |  0.0023571587 |             f
   514 |     5170 |     40 |  0.0023571587 |             f
   515 |     5180 |     40 |  0.0028713793 |             f
   516 |     5190 |     40 |  0.000000E+00 |             f
   517 |     5200 |     40 |  0.0001392758 |             f
   518 |     5210 |     40 |  0.0004106989 |             f
   519 |     5220 |     40 |  0.0004106989 |             f
   520 |     5230 |     40 |  0.0009570934 |             f
   521 |     5240 |     40 |  0.0009995901 |             f
   522 |     5250 |     40 |  0.0018372681 |             f
   523 |     5260 |     40 |  0.0018372681 |             f
   524 |     5270 |     40 |  0.0018372681 |             f
   525 |     5280 |     40 |  0.0019874385 |             f
   526 |     5290 |     40 |  0.0022120527 |             f
   527 |     5300 |     40 |  0.0027932961 |         nadir
   528 |     5310 |     40 |  0.0009230703 |             f
   529 |     5320 |     40 |  0.0011974924 |             f
   530 |     5330 |     40 |  0.0011974924 |             f
   531 |     5340 |     40 |  0.0011974924 |             f
   532 |     5350 |     40 |  0.0011974924 |             f
   533 |     5360 |     40 |  0.0018062270 |             f
   534 |     5370 |     40 |  0.0018989338 |             f
   535 |     5380 |     40 |  0.0019702579 |             f
   536 |     5390 |     40 |  0.0027063979 |             f
   537 |     5400 |     40 |  0.0009520265 |             f
   538 |     5410 |     40 |  0.0009520265 |             f
   539 |     5420 |     40 |  0.0199430199 |         nadir
   540 |     5430 |     40 |  0.0000356125 |             f
   541 |     5440 |     40 |  0.0000356125 |             f
   542 |     5450 |     40 |  0.0003563977 |             f
   543 |     5460 |     40 |  0.0007783096 |             f
   544 |     5470 |     40 |  0.0007783096 |             f
   545 |     5480 |     40 |  0.0010804174 |             f
   546 |     5490 |     40 |  0.0011160300 |             f
   547 |     5500 |     40 |  0.0015706792 |             f
   548 |     5510 |     40 |  0.0015706792 |             f
   549 |     5520 |     40 |  0.0020239168 |             f
   550 |     5530 |     40 |  0.0020239168 |             f
   551 |     5540 |     40 |  0.0030045177 |             f
   552 |     5550 |     40 |  0.0005797099 |             f
   553 |     5560 |     40 |  0.0005797099 |             f
   554 |     5570 |     40 |  0.0005797099 |             f
   555 |     5580 |     40 |  0.0011655043 |             f
   556 |     5590 |     40 |  0.0154277700 |         nadir
   557 |     5600 |     40 |  0.0000350631 |             f
   558 |     5610 |     40 |  0.0002375480 |             f
   559 |     5620 |     40 |  0.0002375480 |             f
   560 |     5630 |     40 |  0.0008490677 |             f
   561 |     5640 |     40 |  0.0015304378 |             f
   562 |     5650 |     40 |  0.0017844976 |             f
   563 |     5660 |     40 |  0.0028129395 |         nadir
   564 |     5670 |     40 |  0.000000E+00 |             f
   565 |     5680 |     40 |  0.0000703561 |             f
   566 |     5690 |     40 |  0.0003185791 |             f
   567 |     5700 |     40 |  0.0013539664 |             f
   568 |     5710 |     40 |  0.0021155088 |             f
   569 |     5720 |     40 |  0.0171673820 |         nadir
   570 |     5730 |     40 |  0.0002503577 |             f
   571 |     5740 |     40 |  0.0004702046 |             f
   572 |     5750 |     40 |  0.0005351668 |             f
   573 |     5760 |     40 |  0.0008928206 |             f
   574 |     5770 |     40 |  0.0011887326 |             f
   575 |     5780 |     40 |  0.0015122281 |             f
   576 |     5790 |     40 |  0.0015122281 |             f
   577 |     5800 |     40 |  0.0021952816 |             f
   578 |     5810 |     40 |  0.0023025778 |             f
   579 |     5820 |     40 |  0.0030122771 |             f
   580 |     5830 |     40 |  0.000000E+00 |             f
   581 |     5840 |     40 |  0.0001430615 |             f
   582 |     5850 |     40 |  0.0002861230 |             f
   583 |     5860 |     40 |  0.0002861230 |             f
   584 |     5870 |     40 |  0.0002861230 |             f
   585 |     5880 |     40 |  0.0002861230 |             f
   586 |     5890 |     40 |  0.0004654802 |             f
   587 |     5900 |     40 |  0.0004654802 |             f
   588 |     5910 |     40 |  0.0005017924 |             f
   589 |     5920 |     40 |  0.0010103436 |             f
   590 |     5930 |     40 |  0.0011087624 |             f
   591 |     5940 |     40 |  0.0011445278 |             f
   592 |     5950 |     40 |  0.0014679670 |             f
   593 |     5960 |     40 |  0.0021452516 |             f
   594 |     5970 |     40 |  0.0021452516 |             f
   595 |     5980 |     40 |  0.0021813218 |             f
   596 |     5990 |     40 |  0.0026737766 |             f
   597 |     6000 |     40 |  0.0000357654 |             f
   598 |     6010 |     40 |  0.0004704675 |             f
   599 |     6020 |     40 |  0.0004704675 |             f
   600 |     6030 |     40 |  0.0008416658 |             f
   601 |     6040 |     40 |  0.0014911945 |             f
   602 |     6050 |     40 |  0.0015627253 |             f
   603 |     6060 |     40 |  0.0015627253 |             f
   604 |     6070 |     40 |  0.0015627253 |             f
   605 |     6080 |     40 |  0.0015627253 |             f
   606 |     6090 |     40 |  0.0015627253 |             f
   607 |     6100 |     40 |  0.0017779036 |             f
   608 |     6110 |     40 |  0.0018758314 |             f
   609 |     6120 |     40 |  0.0018758314 |             f
   610 |     6130 |     40 |  0.0020023538 |             f
   611 |     6140 |     40 |  0.0020381192 |             f
   612 |     6150 |     40 |  0.0022169461 |             f
   613 |     6160 |     40 |  0.0022985792 |             f
   614 |     6170 |     40 |  0.0027325365 |             f
   615 |     6180 |     40 |  0.000000E+00 |             f
   616 |     6190 |     40 |  0.0006403186 |             f
   617 |     6200 |     40 |  0.0006403186 |             f
   618 |     6210 |     40 |  0.0006403186 |             f
   619 |     6220 |     40 |  0.0006403186 |             f
   620 |     6230 |     40 |  0.0006403186 |             f
   621 |     6240 |     40 |  0.0006403186 |             f
   622 |     6250 |     40 |  0.0006403186 |             f
   623 |     6260 |     40 |  0.0006403186 |             f
   624 |     6270 |     40 |  0.0006760840 |             f
   625 |     6280 |     40 |  0.0006760840 |             f
   626 |     6290 |     40 |  0.0008333410 |             f
   627 |     6300 |     40 |  0.0008333410 |             f
   628 |     6310 |     40 |  0.0008333410 |             f
   629 |     6320 |     40 |  0.0014947267 |             f
   630 |     6330 |     40 |  0.0017635353 |             f
   631 |     6340 |     40 |  0.0024243355 |             f
   632 |     6350 |     40 |  0.0027962960 |             f
   633 |     6360 |     40 |  0.000000E+00 |             f
   634 |     6370 |     40 |  0.000000E+00 |             f
#print(res.history[0].pop.get("F"))

11.5. Analysis of Results#

import plotly.express as px

fig = px.scatter(res.F, x=0, y=1, labels={'0': 'Efficiency', '1': 'Volume'},
                    title="In Efficiency vs Volume",
                    width=800, height=800)
fig.update_traces(marker=dict(size=8,
                              line=dict(width=1,
                                        color='DarkSlateGrey')),
                    selector=dict(mode='markers'))
fig.show()
# Making a animation of evolution
import pandas as pd
import plotly.express as px
obj1 = []
obj2 = []
calls = []
for r in res.history:

    objs = r.pop.get("F")
    obj1.extend(objs[:, 0])
    obj2.extend(objs[:, 1])
    calls.extend([r.n_gen]*len(objs))
df = pd.DataFrame(data = {"InEfficiency": obj1, "Volume": obj2, "n_gen": calls})

obj_fig = px.scatter(df, x="InEfficiency", y="Volume",
                        animation_frame="n_gen", color="n_gen",
                        range_x=[0., 0.6], range_y=[0. , 400.],
                        hover_data = df.columns,
                        width = 800, height = 800)
obj_fig.update(layout_coloraxis_showscale=False)
obj_fig.layout.updatemenus[0].buttons[0].args[1]["frame"]["duration"] = 10
obj_fig.update_layout(transition = {'duration': 0.001})
obj_fig.show()

11.6. Exercise#

  • Can you plot the hypervolume metric to see if the convergence is reached

  • Can you implement a termination criterion

  • Plot the optimal configuration of the tracker corresponding to that point

  • Do analysis of convergence

  • Visualize the point with a radar or petal diagram, following https://pymoo.org/visualization/index.html